Home > Calculus > Determining Points of Inflection for a Function

What are the points of inflection, if any, of #f(x)=-3x^3+270x^2-3600x+18000 #?

Answer 1

Emma Aldridge

At #x=30#, there is a point of inflection

Given -

#y=-3x^3+270x^2-3600x+18000#

We must set the send derivative to zero in order to determine the point of inflection.

#dy/dx=9x^2+540x-3600#

#(d^2y)/(dx^2)=18x+540#

Set #(d^2y)/(dx^2)=0#

Then -

#18x+540=0# #x=540/18=30#

At #x=30#, there is a point of inflection

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emily Ammerman

To find the points of inflection, we first need to find the second derivative of the function and then solve for the values of x where the second derivative equals zero or is undefined.

The first derivative of ( f(x) ) is: ( f'(x) = -9x^2 + 540x - 3600 )

The second derivative of ( f(x) ) is: ( f''(x) = -18x + 540 )

Setting ( f''(x) ) equal to zero and solving for x: ( -18x + 540 = 0 ) ( x = 30 )

So, the point of inflection is ( (30, f(30)) ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.